Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 Workspace Analysis in Multirobot Manipulation

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International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002

Workspace Analysis in Multirobot Manipulation

Ramon Costa-Castelló, Luis Basañez

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CONTENTS

Introduction Basic Definitions Multirobot System Analysis

Dexterous Workspace Reachable Workspace

Application to RX-90 robot Dexterous Figure Construction Reachable Figure Construction

Two RX-90 cell Conclusions

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INTRODUCTION

Multirobot Cell

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INTRODUCTION

Multirobot Manipulation Advantages Load Capacity Increase

Dexterity Improvement

Flexible Objects

Multirobot Manipulation Drawbacks Coordination Needed

Workspace Reduction

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INTRODUCTION

Workspace Approaches Analytical Methods

• Singularity Analysis• Exact approach

Volumetric Methods• Workspace discretization• Approximation• Obstacles

Intersection Approach • Intersection of several geometric figures• Quicker approach• Work cell Design capabilities

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CONTENTS

Introduction

Basic Definitions Multirobot System Analysis




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The kinematics f of a mechanism is the relation between the configuration space C and the operational space O

Workspace: elements of O in which the robot end-effector can be placed in

Reachable Workspace: set of positions reachable by the robot end-effector in at least one orientation

Dexterous workspace: set of positions reachable by the robot in all orientations

BASIC DEFINITIONS

f C O

|W x O C x f

| ( )nRW p R x R p W R SO n

| ( )nDW p R x W x R p R SO n

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CONTENTS

Introduction Basic Definitions

Multirobot System Analysis Dexterous Workspace Reachable Workspace



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MULTIROBOT SYSTEMS ANALYSIS

0 0 0 0 1c i i i iC C C i N

i i i iB f O Individual kinematics

Multirobot System Configuration Space

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0

0

0

0

i i i i i i

i i i

f B f i O B f i B

f B f i O

p R R p R p p

R R R R

Position and Orientation Constraining Equations

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MULTIROBOT SYSTEMS ANALYSISDexterous Workspace

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0

0 0| ( )

1i i ii i

o

nD i i

O B Bf

f

W x R R SO n C C

Rp R p p x i N

p x

Dexterous Workspace Definition

Expression Manipulation


iDOB

TB

iDBOB

BiDBO

WpRpxRR

WRpRpxR

pWRpRxR

iii

iii

iii

,

,

,

iDOB

TB WppxRsph

iii ,

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Workspace

Dexterous Figure

Dexterous Figure definition

Dexterous Workspace from Dexterous Figure


iDOBTB

iD

iD WppxRsphWxW

iii ,|ˆ

Ni

DiDD WWW

..1

0ˆ

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MULTIROBOT SYSTEMS ANALYSISReachable Workspace

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i oR R RW W W

Reachable Space Approximation

Reachable Figure Definition

Reachable Workspace from Reachable Figure

ReachableFigure

Workspace

MULTIROBOT SYSTEMS ANALYSISReachable Figure

0| , i i i i

n T iR R O O B R BW x R x W R x RR p R W p

| i i i i

i n T iR O O B R BW x R R x RR p R W p

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CONTENTS





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RX-90 robot

APPLICATION TO RX-90 ROBOT

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RX-90 Configuration Space section

RX-90 Work Space section1 ctt

1 ctt


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RX-90 3D WorkspaceRX-90 selected sections


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RX-90 Dexterous Figure Construction Scheme

APPLICATION TO RX-90 ROBOTDexterous Workspace

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Reachable figure for

APPLICATION TO RX-90 ROBOTReachable Figure

mmpiO

50

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APPLICATION TO RX-90 ROBOTReachable Figure

Reachable figure for mmpiO

2000

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CONTENTS





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1

1 0 0 500

0 1 0 0

0 0 1 461

0 0 0 1

mm

Omm

Cell Picture

TWO RX-90 CELL

1

1 0 0 846

0 1 0 1306

0 0 1 0

0 0 0 1

mm

mmB

mmpiO

08.680

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Reference Robot Workspace and Reachable Figure

TWO RX-90 CELL

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31 193534m 46 36%

TWO RX-90 CELLReachable Workspace

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CONTENTS




Two RX-90 cell

Conclusions

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• A new method to analyze multirobot workspace has been presented. The method is based in computing the intersection of the reference manipulator workspace and the reachable/dexterous figure of the other robots.

• The method has been applied to PUMA like manipulators.

• Further work : Introduction of orientation kinematics.

CONCLUSIONS

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Robots in the same Position and different Orientation

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Orientation Range Analysis

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Further Works

Orientation Range Analysis through Analytic Methods

Automatic Work Cell Design (Position and Orientation)

Documents

Workspace Analysis in Multirobot Manipulation International Symposium on Robotics Stockholm, Sweden. Oct 7-11, 2002 Workspace Analysis in Multirobot Manipulation